Lattice field theory simulations of graphene

TL;DR

This paper uses lattice field theory simulations to study the semimetal-insulator transition in graphene, providing insights into the critical behavior and phase transition nature through Monte Carlo methods.

Contribution

It applies Monte Carlo simulation techniques to lattice field theories of graphene, analyzing the phase transition and critical exponents with detailed finite-size effects discussion.

Findings

Evidence for an insulating phase in suspended graphene

The transition is likely second order but without classical critical exponents

Results challenge the Miransky scaling prediction

Abstract

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.